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The application of deep learning in time-series prediction has developed gradually. In this paper, we propose a deep generative network model for feature extraction of multivariate time series, namely, mutual information variational autoencoders (MI-VAE). In the architecture of the proposed model, we use the latent space of VAE for feature learning, which can extract the essential features of multivariate time-series data effectively. The latent space employed directly as a feature extractor can avoid poor interpretability of model. In addition, we introduce a mutual information term into the loss function, which improves the expression capability and accuracy of model. The proposed model, combining the merits of VAE and mutual information, extracts features for multivariate time-series data from a new perspective. The Lorenz system and Beijing air quality time series are used to test performance of the proposed model and comparative models. Results show that the proposed model is superior to other similar models in terms of accuracy and expression capability of latent space. [ABSTRACT FROM AUTHOR]

A precise and timely classification of particulate matter 2.5 concentration levels is important for the design of air quality regulatory measures in a contemporaneous context characterized by the transition to a low-carbon economy. This study uses a well-known air quality dataset retrieved from the University of California at Irvine repository, which consists of a multivariate time series covering particulate matter 2.5 concentration levels in the city of Beijing for a period of 5 years. We train, test, and validate several deep learning architectures for a multinomial classification of the target variable in the period of 24 h ahead from the contemporaneous moment of action relying on historical information about the last 168 h and considering a sliding window of 24 h to construct examples. Results indicate that the internationally patented Variable Split Convolutional Attention model exhibits the best accuracy. The main novelty of this model consists of introducing bidimensional convolutional operations inside the attention block to capture the relative attention weight given to patterns of contiguous segments within different time-steps for each input variable. Therefore, a valuable deep learning architecture is presented to properly classify particulate matter 2.5 concentration levels in the atmosphere. • 2D input map transformed into a 3D input (Variables × Time-Steps × Segments) map. • 3D map embraces a cyclical segmentation of the input set by explanatory variable. • Splitting process to build attention maps per explanatory variable boosts precision. • For each attention block, 2D maps of attention weights using convolutional layers. • Case-study uses PM2.5 dataset provided by UCI and considers a target with 5 levels. [ABSTRACT FROM AUTHOR]

• An imputation model imputes specific missing values in multivariate time series. • Our method outperforms the comparison method when specific values are missing. • Our experiments provide selection principles of hyperparameters. • Our experiment determines the best training method with introduction of noise. Data missing is a ubiquitous phenomenon in multivariate time series analysis because of failure measurements, improper installation or other unfavorable factors. Most imputation methods, such as statistical methods and machine learning methods, are mainly for dealing with random or continuous missing, but do not take into consideration the non-random specific missing situation. This paper proposes an imputation model based on the variational auto-encoders (VAE) and shift correction for specific missing values, which is also extended to the β -VAE model. The shift correction is used to correct the original probability distribution deviation caused by specific values concentrated missing. Then taking the meteorological and air quality data sets in Beijing as the example, this paper mainly explores two common specific missing situations, including large values missing and small values missing. The experimental results show that the proposed model can effectively impute specific missing values, which has high imputation accuracy and robustness. [ABSTRACT FROM AUTHOR]